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• W2006712105 abstract "The martingale problems provide a powerful tool for characterizing Markov processes, especially in addressing convergence issues. For each n, let metric space E-valued process Xn be a solution of the An martingale problems (i.e.f(Xn(t))−f(Xn(0))−∫0tAnf(Xn(s))dsis a martingale), the convergence of Anf→Af in some sense usually implies the weak convergence of Xn⇒X, where X is some process characterized by A. Our goal here is to establish similar results for another type of limit theorem – large deviations: defining Hnf=e−fAnef, thenexpf(Xn(t))−f(Xn(0))−∫0tHnf(Xn(s))dsis a martingale. We prove that the convergence of nonlinear operators 1nHn(nf)→Hf implies the large deviation principle for the Xns, where the rate function is characterized by a nonlinear transformation L of H. Furthermore, a ‘running cost’ interpretation from control theory can be given to this function. The main assumption is a regularity condition on H in the sense that for each f0∈D(H), bounded viscosity solution of−∂tu(t,x)+(Hu(t,·))(x)=0;u(0,x)=f0(x)is unique. This paper considers processes in CE[0,T]." @default.
• W2006712105 created "2016-06-24" @default.
• W2006712105 creator A5050292971 @default.
• W2006712105 date "1999-06-01" @default.
• W2006712105 modified "2023-10-12" @default.
• W2006712105 title "Martingale problems for large deviations of Markov processes" @default.
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• W2006712105 doi "https://doi.org/10.1016/s0304-4149(98)00104-5" @default.
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